normalizedBanzhafValue {CoopGame}

Compute normalized Banzhaf value

Description

normalizedBanzhafValue computes the normalized Banzhaf value for a specified TU game. The corresponding formula can e.g. be found in the article by Stach (2017), p. 77.

Usage

normalizedBanzhafValue(v)

Arguments

v

Numeric vector of length 2^n - 1 representing the values of the coalitions of a TU game with n players

Value

The return value is a numeric vector which contains the normalized Banzhaf value for each player.

Author(s)

Jochen Staudacher [e-mail]

References

Gambarelli G. (2011) "Banzhaf value", Encyclopedia of Power, SAGE Publications, pp. 53–54

Stach I. (2017) "Sub-Coalitional Approach to Values", In: Nguyen, N.T. and Kowalczyk, R. (Eds.): Transactions on Computational Collective Intelligence XXVI, Springer, pp. 74–86

Examples

library(CoopGame)
normalizedBanzhafValue(c(0,0,0,1,2,3,6))


#Example from paper by Gambarelli (2011)
library(CoopGame)
v=c(0,0,0,1,2,1,3)
normalizedBanzhafValue(v)
#[1] 1.1538462 0.6923077 1.1538462
#Expected Result: 15/13  9/13  15/13